Match List-I with List-II
| List-I | List-II | ||
| Product | Last two digits | ||
| (A) | 5632 × 741 | (I) | 64 |
| (B) | 39914 × 5346 | (II) | 44 |
| (C) | 4443 × 944 | (III) | 12 |
| (D) | 5009 × 996 | (IV) | 92 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (III), (B) - (II), (C) - (IV), (D) - (I)
The last two digits of a product are the product modulo 100, and they depend only on the last two digits of each factor: if \( a\equiv a' \pmod{100} \) and \( b\equiv b' \pmod{100} \), then \( ab\equiv a'b' \pmod{100} \).
(A) 5632 × 741
This matches (III) 12.
\( \displaystyle 32\times 41=1312\ \Rightarrow\ \text{last two digits}\ 12 \)
(B) 39914 × 5346
This matches (II) 44.
\( \displaystyle 14\times 46=644\ \Rightarrow\ \text{last two digits}\ 44 \)
(C) 4443 × 944
This matches (IV) 92.
\( \displaystyle 43\times 44=1892\ \Rightarrow\ \text{last two digits}\ 92 \)
(D) 5009 × 996
This matches (I) 64.
\( \displaystyle 9\times 96=864\ \Rightarrow\ \text{last two digits}\ 64 \)
So the matching is (A)-(III), (B)-(II), (C)-(IV), (D)-(I).